The Spitalfields area of East London on a Sunday morning is fab and with a great deal of interesting history. It goes back many centuries and was where immigrant communities first settled, first the Hugenots who built the elegant houses for their silk-weaving, then Jewish settlers from Eastern Europe, now folks from the Horn of Africa and Bangladesh.
Huge street markets in Petticoat Lane and Brick Lane, loads of ethnic food, many old houses and streets. Also a flower market in nearly Columbia Road. While you can visit any time of course, Sunday morning is the day for the action in Brick Lane and Petticoat Lane so far as I can tell. The
flower market in Columbia Road opens very early and closes early too. The activity is all in the morning. The area is also plastered with Banksy-style street art on walls and buildings (though not by Banksy himself these days, I guess, as his work has become far too valuable).
A walk along the
South Bank from London Bridge to Waterloo, starting at Borough market (photogenic and quite tasty at weekends) by Southwark Cathedral, taking in the vast Tate Modern gallery, the Globe Theatre, the South Bank complex and Royal Festival Hall, etc. Great views across the Thames if there is a nice sunset or late afternoon light. Plenty of places to stop for coffee and a break, etc. Halfway along there is a modern pedestrian bridge over the river taking you direct to St Paul's Cathedral. A good spot for a cityscape pic or two.
London's Parks, particularly (imho) Regent's Park.
The City financial district for some skyscrapers and modern architecture, plus the Tower of London and some historic old buildings. Some skyscrapers have top-floor bars or eateries with amazing views. Trip Advisor or a similar site might have some details.
Some good eighteenth century squares and housing in the area around the British Museum in Bloomsbury.
Soho and Chinatown for a walk through an old quarter (now much cleaned up of the red light riff-raff that used to flourish there many years ago). It's now full of younger folks hanging out, cafes and so forth. Nearby there is Covent Garden with a few interesting streets but imho a bit of an overcrowded shopping hell these days.
Coffee in the
Photographer's Gallery just behind Oxford Street Tube Station. Ground floor cafe, nice photography bookshop downstairs and usually an interesting exhibition or two upstairs.
Many smaller, interesting museums and galleries like the
Wallace Collection or the
Sir John Soane Museum - in addition to the larger and well-known ones. Some say the Soane museo is one of London's hidden gems.
I use lenses of 15-40mm typically, sometimes a 70mm. All DA primes in my case. Wide-ish angles are definitely on the menu with architecture, views across rivers and parks and so forth.
Yes, Notting Hill is another area to put on the menu I guess. Kew Gardens is a superb place for botanical things but it is quite a way from the centre of London and so with getting a train there it would take up at least half a day, probably most of a day.
If you have time for a day out then Brighton or Oxford (where I live) are easy to get to and full of life.
Ps: Someone has just told me that taking a riverboat from central London to the National Maritime Museum at Greenwich is a good and easy trip.
Hope you have a great trip.